Wall Solution with Weak Gravity Limit in Five Dimensional Supergravity

In five-dimensional supergravity, an exact solution of BPS wall is found for a gravitational deformation of the massive Eguchi-Hanson nonlinear sigma model. The warp factor decreases for both infinities of the extra dimension. Thin wall limit gives the Randall-Sundrum model without fine-tuning of input parameters. We also obtain wall solutions with warp factors which are flat or increasing in one side, by varying a deformation parameter of the potential. e-mail address: [email protected] e-mail address: [email protected] e-mail address: [email protected] e-mail address: [email protected] Introduction One of the most interesting models in the brane-world scenario is given by Randall and Sundrum, where the localization of four-dimensional graviton [1] has been obtained by a spacetime metric containing a warp factor e which decreases exponentially for both infinities of the extra dimension y → ±∞ ds = gμνdx dx = eηmndx dx + dy, (1) where μ, ν = 0, .., 4, m,n = 0, 1, 3, 4 and y ≡ x. They had to introduce both a bulk cosmological constant and a boundary cosmological constant, which have to be fine-tuned each other. Its supersymmetric (SUSY) version has been worked out [2], and has been argued to help understanding the fine-tuning [3]. Since the Randall-Sundrum model uses the bulk AdS space, it has implications for the AdS/CFT correspondence [4], [5]. For that purpose it is also natural to introduce scalar fields forming a smooth wall (thick brane) in supergravity theories. After an extensive studies of BPS walls in four-dimensional supergravity coupled with chiral scalar multiplets [6], an exact solution of a BPS wall has recently been constructed [7]. Studies of domain wall solutions in gauged supergravity theories in five dimensions revealed that hypermultiplets are needed [8] to obtain warp factors decreasing for both infinities y → ±∞ (infra-red (IR) fixed points in AdS/CFT correspondence) which are appropriate for phenomenology. It has been shown that the target space of hypermultiplets in fivedimensional supergravity theory must be quaternionic Kähler manifolds [9] in contrast to the hyper-Kähler target space for five-dimensional global SUSY without gravity. The gravitational deformations have been worked out for massless N = 2 nonlinear sigma models in four dimensions [10], [11]. However, massive models, namely models with potential terms are needed to obtain domain wall solutions. Massive hyper-Kähler nonlinear sigma models without gravity in four dimensions have been constructed in harmonic superspace as well as in N = 1 superfield formulation [12], and have yielded the domain wall solution for the Eguchi-Hanson manifold [13] previously obtained in the on-shell component formulation [14]. Domain walls in massive quaternionic Kähler nonlinear sigma models in supergravity theories have been studied using mostly homogeneous target manifolds. Unfortunately, SUSY vacua in homogeneous target manifolds are not truly IR critical points, but can only be saddle points with some IR directions [15], [16]. Inhomogeneous manifolds and a wall solution have also been constructed [17]. However, these manifolds do not allow a limit of weak gravitational coupling, contrary to the model with an exact solution in four-dimensions [7]. The purpose of our paper is to present an exact BPS domain wall solution in fivedimensional supergravity coupled with hypermultiplets (and vector multiplets). We have obtained a two-parameter family of massive quaternionic nonlinear sigma models which reduces to the Eguchi-Hanson nonlinear sigma model for vanishing gravitational coupling. One of the parameters is the gravitational coupling κ, and the other is an asymmetry parameter a for gravitational deformation of potential terms. Having a smooth limit of vanishing gravitational coupling is very useful to obtain inhomogeneous quaternionic Kähler manifolds and also to use it for brane-world phenomenology. The model has two SUSY vacua as genuine local minima up to a critical value of gravitational coupling